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A General Distribution for Describing Security Price Returns

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  • Bookstaber, Richard M
  • McDonald, James B

Abstract

This paper introduces a generalized distribution, called the GB2 distribution, for describing security returns. The distribution is extremely flexible, containing a large number of well-known distributions, such as the lognormal, log-t, and log-Cauchy distribu tions, as special or limiting cases and allowing large, even infinite, higher moments. This flexibility allows a direct representation of different degrees of fat tails in the distribution. The properties of the GB2 make it useful in empirical estimation of security returns and in facilitating the development of option-pricing models and other models that depend on the specification and mathematical manipulation of distributions. Copyright 1987 by the University of Chicago.

Suggested Citation

  • Bookstaber, Richard M & McDonald, James B, 1987. "A General Distribution for Describing Security Price Returns," The Journal of Business, University of Chicago Press, vol. 60(3), pages 401-424, July.
  • Handle: RePEc:ucp:jnlbus:v:60:y:1987:i:3:p:401-24
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    Cited by:

    1. Liu, Xiaoquan & Shackleton, Mark B. & Taylor, Stephen J. & Xu, Xinzhong, 2007. "Closed-form transformations from risk-neutral to real-world distributions," Journal of Banking & Finance, Elsevier, vol. 31(5), pages 1501-1520, May.
    2. Chung, San-Lin & Wang, Yaw-Huei, 2008. "Bounds and prices of currency cross-rate options," Journal of Banking & Finance, Elsevier, vol. 32(5), pages 631-642, May.
    3. Paul Larsen, 2015. "Asyptotic Normality for Maximum Likelihood Estimation and Operational Risk," Papers 1508.02824, arXiv.org, revised Aug 2016.
    4. Cummins, J. David & McDonald, James B. & Merrill, Craig, 2007. "Risky Loss Distributions and Modeling the Loss Reserve Pay-out Tail," Review of Applied Economics, Review of Applied Economics, vol. 3(1-2).
    5. Kabir K. Dutta & David F. Babbel, 2005. "Extracting Probabilistic Information from the Prices of Interest Rate Options: Tests of Distributional Assumptions," The Journal of Business, University of Chicago Press, vol. 78(3), pages 841-870, May.
    6. Gene L. Leon & Rupert D Worrell, 2001. "Price Volatility and Financial Instability," IMF Working Papers 01/60, International Monetary Fund.
    7. repec:ris:utmsje:0199 is not listed on IDEAS
    8. James F. Moore, 1999. "Tail Estimation and Catastrophe Security Pricing: Can We Tell What Target We Hit if We Are Shooting in the Dark?," Center for Financial Institutions Working Papers 99-14, Wharton School Center for Financial Institutions, University of Pennsylvania.
    9. Trino-Manuel Niguez & Ivan Paya & David Peel & Javier Perote, 2013. "Higher-order moments in the theory of diversification and portfolio composition," Working Papers 18297128, Lancaster University Management School, Economics Department.
    10. Minenna, Marcello, 2003. "Insider trading, abnormal return and preferential information: Supervising through a probabilistic model," Journal of Banking & Finance, Elsevier, vol. 27(1), pages 59-86, January.
    11. Jackwerth, Jens Carsten, 1999. "Option Implied Risk-Neutral Distributions and Implied Binomial Trees: A Literature Review," MPRA Paper 11634, University Library of Munich, Germany.
    12. Dilip B. Madan & Frank Milne, 1991. "Option Pricing With V. G. Martingale Components," Mathematical Finance, Wiley Blackwell, vol. 1(4), pages 39-55.
    13. Adcock, C.J. & Shutes, K., 2005. "An analysis of skewness and skewness persistence in three emerging markets," Emerging Markets Review, Elsevier, vol. 6(4), pages 396-418, December.
    14. Mookerjee, Rajen & Yu, Qiao, 1999. "An empirical analysis of the equity markets in China," Review of Financial Economics, Elsevier, vol. 8(1), pages 41-60, June.
    15. Leonidas Tsiaras, 2010. "Dynamic Models of Exchange Rate Dependence Using Option Prices and Historical Returns," CREATES Research Papers 2010-35, Department of Economics and Business Economics, Aarhus University.
    16. Marcos Massaki Abe & Eui Jung Chang & Benjamin Miranda Tabak, 2007. "Forecasting Exchange Rate Density Using Parametric Models: the Case of Brazil," Brazilian Review of Finance, Brazilian Society of Finance, vol. 5(1), pages 29-39.
    17. Fabozzi, Frank J. & Leccadito, Arturo & Tunaru, Radu S., 2014. "Extracting market information from equity options with exponential Lévy processes," Journal of Economic Dynamics and Control, Elsevier, vol. 38(C), pages 125-141.
    18. Kabir K. Dutta & David F. Babbel, 2002. "On Measuring Skewness and Kurtosis in Short Rate Distributions: The Case of the US Dollar London Inter Bank Offer Rates," Center for Financial Institutions Working Papers 02-25, Wharton School Center for Financial Institutions, University of Pennsylvania.
    19. Bisht Deepak & Laha, A. K., 2017. "Assessment of Density Forecast for Energy Commodities in Post-Financialization Era," IIMA Working Papers WP 2017-07-01, Indian Institute of Management Ahmedabad, Research and Publication Department.
    20. Kabir Dutta & Jason Perry, 2006. "A tale of tails: an empirical analysis of loss distribution models for estimating operational risk capital," Working Papers 06-13, Federal Reserve Bank of Boston.
    21. Josip Arneric & Zdravka Aljinovic & Tea Poklepovic, 2015. "Extraction of market expectations from risk-neutral density," Zbornik radova Ekonomskog fakulteta u Rijeci/Proceedings of Rijeka Faculty of Economics, University of Rijeka, Faculty of Economics, vol. 33(2), pages 235-256.
    22. Ha, Daesung & Chang, S. J., 1998. "The distribution of transaction intervals in common stock trading," International Review of Economics & Finance, Elsevier, vol. 7(1), pages 103-115.
    23. Takkabutr, Nattapol, 2013. "Option-Implied Risk Aversion Anomalies: Evidence From Japanese Market," Hitotsubashi Journal of Economics, Hitotsubashi University, vol. 54(2), pages 137-157, December.
    24. Hans Dillen & Bo Stoltz, 1999. "The distribution of stock market returns and the market model," Finnish Economic Papers, Finnish Economic Association, vol. 12(1), pages 41-56, Spring.
    25. José Renato Haas Ornelas & Marcelo Yoshio Takami, 2011. "Recovering Risk-Neutral Densities from Brazilian Interest Rate Options," Brazilian Review of Finance, Brazilian Society of Finance, vol. 9(1), pages 9-26.

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